The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling

Abstract

The refractive indices of AlxGa1−xAs epitaxial layers (0.176⩽x⩽1) are accurately determined below the band gap to wavelengths, λ<3 μm. The layers are grown on GaAs substrates by molecular beam epitaxy metal organic and chemical vapor deposition with thicknesses ranging from 4 to 10 μm. They form improper waveguide structures with the GaAs substrate. The measurements are based on the excitation of the improper waveguide modes with grating couplers at 23 °C. The refractive indices of the layers are derived from the modal propagation constants in the range of 730 nm<λ<830 nm with an estimated uncertainty of Δn=5×10−4. The temperature coefficient of the refractive index is investigated in the same spectral range. From the effective indices of the TE and TM modes, we derive the strain-induced birefringence and the elasto-optic coefficients. High-resolution x-ray diffraction is used to determine the strain of the layers. The layer compositions are obtained with inductively coupled plasma atomic emission spectroscopy. The measurement range of the refractive index is extended from the direct gap to λ<3 μm by observing the Fabry-Pérot interference fringes of the transmission spectra of isolated layers. The measured values of the refractive index and the elasto-optic coefficient are compared to calculated data based on semiempirical models described in the literature. Published data of the index of refraction on GaAs, AlAs and GaP are analyzed to permit the development of a modified Sellmeier approximation. The experimental data on AlxGa1−xAs can be fitted over the entire composition range 0⩽x⩽1 to provide an accurate analytical description as a function of composition, wavelength, and temperature.

Diffraction of Quantum Dots Reveals Nanoscale Ultrafast Energy Localization

“…For GaAs at 300 K, the de Broglie wavelength of the conduction electrons is , = 2.ℏ /201 2 ⁄ ≈ 30 nm, where 2 = 300 K, ℏ the Planck constant, 1 the Boltzmann constant, 0 = 0.0670 the electron effective mass, and 0 is the free-electron mass. When the dot size is smaller than , , quantum confinement effects become relevant, giving rise to a discrete energy spectrum and an increasing S3 inter-band separation, 8 , for a decreasing dot size, as shown in Figure S1B, which also displays the results of ab initio calculations 4,5 .…”

“…The FDTD simulations predict that for dot dimensions smaller than the photon wavelength, the fraction, , of laser intensity absorbed by the dot decreases for a decreasing size. On the other hand, for a decreasing dot size, the energy gap, 8 , gets closer to the photon energy, approaching the condition for a resonant electronic excitation, which is described by the relevant increase of the factor ! " #$ !…”

“…However, we have also calculated the distribution of the electric field inside and outside the dot as induced by the incident laser. This has been obtained by means of Finite Difference Time Domain (FDTD) simulations 7 and the results are plotted in Figure S2A-F. We used the experimental bulk dielectric constants taken from the literature for both the AlGaAs substrate 8 and the GaAs dots 9 . Illumination is provided by a plane wave source and the mesh size within and around the island is 0.5 nm.…”

Investigation of temperature characteristics of modern InAsP/InGaAsP multi-quantum-well TJ-VCSELs for optical fibre communication

“…The heat−transfer coefficient for the bottom heat−sink surface has been assumed as equal to 50 Wm -2 K -1 . Refractive indices have been reported by Gehrsitz et al [33], Gini and Melchior [34], Chandra et al [35], and Henry et al [36], Lee and Lee [37] or found in www.virginiasemi.com. Temperature−dependent absorption coefficients have been given in [38][39][40][41][42][43][44][45].…”

Enhanced second-harmonic generation from magnetic resonance in AlGaAs nanoantennas

“…1(a), the incident light was a plane wave with a wave vector, k, parallel to the cylinder axis and the electric field, E, polarized along the x-axis. For the dispersion of the refractive index of Al 0.18 Ga 0.82 As we used the analytical model proposed in [18] which was derived from comparison with measurements. The scattering efficiency (defined as Q sca = C sca /πr 2 where C sca is the scattering cross-section and r is the cylinder radius) calculated for a cylinder suspended in air with radius r = 225 nm and height h = 400 nm is shown in Fig.…”